Finite Group Databasebeta

C2×#27165792 #38787072

order25664
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27165792

Splittings

SylowC401 ⋊ C2×#97

Subgroups

subgroupG/H
centerC23C2×#13107944
commutatorC2×C401C2×C42
FrattiniC22C22×#13107944
FittingC22×C4×C401C4
socle, prime radicalC23×C401C2×C4
cosocleC2×Dic401C23
hypercenterC22×C4#13107944
hypocenterC401C2×#97
LCSG ▷ C2×C401 ▷ C401
UCSC1 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25664

Conjugacy classes & character table

1640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25664, 1507);